Impacts of the anomaly on nuclear and neutron star equation of state based on a parity doublet model

Gao, B.*; 南川 拓哉*; 古城 徹*; 原田 正康*

Physical Review C, 106(6), p.065205_1 - 065205_14, 2022/12

https://doi.org/10.1103/PhysRevC.106.065205

We examine the role of the U(1) anomaly in a parity doublet model of nucleons which include the chiral variant and invariant masses. Our model expresses the U(1) anomaly by the Kobayashi-Maskawa-'t Hooft (KMT) interaction in the mesonic sector. After examining the roles of the KMT term in vacuum, we discuss its impacts on nuclear equations of state (EOS). The U(1) anomaly increases the masses of the ' and mesons and enhances the chiral symmetry breaking. Also, the U(1) anomaly enlarges the energy difference between chiral symmetric and symmetry broken vacuum; in turn, the chiral restoration at high density adds a larger energy density (often referred as a bag constant) to EOSs than in the case without the anomaly, leading to softer EOSs. Including these U(1) effects, we update the previously constructed unified equations of state that interpolate the nucleonic EOS at 2 ( = 0.16 fm; nuclear saturation density) and quark EOS at 5 . The unified EOS is confronted with the observational constraints on the masses and radii of neutron stars. The softening of EOSs associated with the (1) anomaly reduces the overall radii, relaxing the previous constraint on the chiral invariant mass . Including the attractive nonlinear - coupling for the reduced slope parameter in the symmetry energy, our new estimate is 400 MeV 700 MeV, with smaller than our previous estimate by 200 MeV.